Computational geometry: an introduction
Computational geometry: an introduction
Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Computing Two-Dimensional Integer Hulls
SIAM Journal on Computing
Digital Planarity of Rectangular Surface Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
A linear incremental algorithm for naive and standard digital lines and planes recognition
Graphical Models - Special issue: Discrete topology and geometry for image and object representation
Discrete Applied Mathematics
An elementary digital plane recognition algorithm
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
A composite and quasi linear time method for digital plane recognition
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Gift-wrapping based preimage computation algorithm
Pattern Recognition
Maximal planes and multiscale tangential cover of 3D digital objects
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
Recognition of digital hyperplanes and level layers with forbidden points
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
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This paper introduces a method for the digital naive plane recognition problem. This method is a revision of a previous one. It is the only method which guarantees an O(n log D) time complexity in the worst-case, where (D - 1) represents the size of a bounding box that encloses the points, and which is very efficient in practice. The presented approach consists in determining if a set of n points in Z3 corresponds to a piece of digital naive hyperplane in ⌊4 log9/5 D⌋ + 10 iterations in the worst case. Each iteration performs n dot products. The method determines whether a set of 106 voxels corresponds to a piece of a digital plane in ten iterations in the average which is five times less than the upper bound. In addition, the approach succeeds in reducing the digital naive plane recognition problem in Z3 to a feasibility problem on a two-dimensional convex function. This method is especially fitted when the set of points is dense in the bounding box, i.e. when D = O(√n).